Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+6, x \in R$,then $f(2)$ equals

The monomer $( X )$ involved in the synthesis of Nylon $6,6$ gives positive carbylamine test. If $10$ moles of $X$ are analyzed using Dumas method, the amount $($in grams$)$ of nitrogen gas evolved is $....$
Use: Atomic mass of $N ($in amu$) = 14$

The number of unpaired electrons in a chromic ion $Cr^{3+}$ (atomic number $= 24$) is

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The magnitude of the induced e.m.f. between the rim and the axis of the disc is:

The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is

Cellulose is a polymer of......